If PMP is a very rare quantile, the immediate question is which one. This now arrives regularly from clients and regulators as a request for the 10,000-year rainfall, or 10⁻⁴ annual exceedance probability, on the assumption that it is broadly equivalent to PMP.
Where the exercise has been carried out in the United States, PMP estimates have been found to correspond to annual exceedance probabilities between 10⁻⁴ and 10⁻⁷. Across a wider set of studies, the AEP of existing PMP estimates has been found to vary by several orders of magnitude, at least for large catchments and long durations.
No single conversion exists, and it has to be derived for the specific project. Modern studies increasingly derive a full AEP curve alongside the deterministic PMP. However, these two quantities as not interchangeable.
On a side note, US practice sense-checks a PMP estimate against the 100-year rainfall for the same duration and area. In past studies the ratio has ranged between two and seven, depending on the distance from the moisture source and the type of terrain.
The structure of a conventional PMP study
Most site-specific studies follow the deterministic hydrometeorological approach, which reduces to four steps. A catalogue of major observed storms is assembled and reduced to depth over a range of areas and durations. The moisture content of each storm is increased to a climatological maximum, conventionally taken two weeks into the warmer season. The maximised storms are transposed to each grid cell, to the extent supportable by similarity of topographic and meteorological conditions. The largest amounts among the maximised and transposed storms give the PMP depths at each duration. The same datasets can be used to derive an annual maximum series, from which probability distributions are fitted and basin-specific AEPs calculated.
The alternative is the statistical approach associated with Hershfield, which estimates PMP from an annual maximum series without reference to individual storms, and is generally applied to small catchments where storm data are sparse.
The following sections take the four steps in turn, with the 2024 criticism and the practical consequence attached to each.
The storm catalogue
Question whether the analysed depths rest on radar or on gauge interpolation. Radar coverage for older storms may be poor or absent, and the distinction matters most for the short-duration, small-area depths that control small catchments.
This is also the part where reproducibility is lost. The method description is published, but outside a handful of jurisdictions there is no public extreme-storm catalogue, so the depth-area-duration results that determine the answer arrive as a proprietary deliverable rather than as something a third party can derive or check. Flood estimation manages this better: deriving a Regional Maximum Flood for a project in southern Africa, we worked from Herschy’s published catalogue of maximum observed floods and a published regionalisation, both of which a reviewer can go and check. Nothing equivalent exists for extreme rainfall in most of the world.
The computation is no longer the constraint. Large language models have reduced the work of turning a published method description into working code from weeks to hours, which leaves the catalogue as the binding limitation.
Moisture maximisation
The moisture content of each storm is raised to a climatological maximum on the assumption that rainfall scales linearly with available moisture and that storm dynamics are independent of it. The 2024 review finds neither assumption supported: observational and modelling work indicates that convergence intensifies as moisture increases, so the two are coupled and the relationship is non-linear. The step is a conservative engineering adjustment, and describing it as physics overstates what it does.
Two inputs carry the judgement: the storm-representative dew point, and the cap applied to the maximisation factor. Both can now be obtained from gridded reanalysis datasets which is the single largest gain in reproducibility available under current methods.
Downloading climate datasets like ERA5 for catchments of interest, soon to be ERA6, and taking the maximisation parameters from it is straightforward for anyone with coding skills and should now be standard.
Transposition limits
Transposition moves a maximised storm from where it occurred to the catchment, on the judgement that the two locations are meteorologically and topographically similar enough for the storm to have occurred at either. The boundary drawn around that region decides which storms are admitted at all, and because PMP is the maximum across the admitted set, including or excluding one large storm can change which storm controls a given duration.
The 2024 review finds that the specification of transposition regions rests on subjective meteorological judgement without a solid scientific foundation, and that sensitivity studies have shown transposition to play a decisive role in the resulting estimate. Few studies report what happens when the boundary is varied.
Testing it means redrawing the boundary, recomputing, and reporting whether the controlling storm at each duration changes. If it does, the depth at that duration rests on a single judgement about meteorological similarity.
Envelopment
The largest adjusted value across all candidate storms is taken for each duration and area, and smoothed into a consistent set of curves. The review’s criticism is that envelopment has never been formalised and is not compatible with a statistical treatment of the depth it produces: it is a maximum drawn from a small and incomplete sample, not an estimator. Modern practice envelopes per grid cell rather than by hand-smoothing idealised elliptical patterns across a catchment, which improves consistency without changing the statistical character of the operation.
Terrain adjustment
Terrain enters at the transposition step and is handled through a single ratio, the Geographic Transposition Factor, computed as the 100-year precipitation depth at the target grid cell divided by the 100-year depth at the storm source. The reasoning is that a precipitation frequency climatology already reflects all the precipitation-producing processes at each location.
The 2024 review is critical of this approach. The factor can replace parts of the moisture transposition function and be applied everywhere, including where terrain is flat, and it remains unverified. It is defensible as a documented calculation; it is not defensible as a demonstrated representation of the orographic effect after which it is named. Extending it to regions that do not require orographic adjustment is specifically discouraged.
Storm type, duration and catchment scale
PMP across a full range of durations and areas is not produced by a single storm. Local storms control smaller areas and durations under about six hours; general storms control longer durations and larger areas, where lower intensity is offset by duration and areal coverage.
Storm type is rarely carried into a hydrological study intended as an input to design, yet the spatial and temporal distribution of rainfall varies by storm type, and it is the distribution rather than the depth alone that governs peak flow and flood volume.
Common practice applies the same disaggregation as for ordinary design rainfall, which assumes the temporal profile of an extreme convective event resembles that of a frequent one.
Where this leaves the method
Modern PMP practice is better documented, more reproducible and more useful than what preceded it, and it increasingly arrives with a probability curve attached. It also rests on a foundation the 2024 review found deficient in several specific respects:
- The assumption that rainfall is bounded.
- No procedure for accounting for the effect of climate change on rainfall extremes.
- Incomplete sampling of extreme rainfall events in storm catalogues, in both time and space.
- Storm transposition procedures that are subjective by construction.
- No sound scientific foundation for moisture maximisation.
- Reliance on empirical correction factors for the effect of complex terrain.
- No procedure for accounting for the statistical uncertainty of the estimates.
The first six are properties of the method. The seventh follows from defining PMP by the procedure used to compute it: if no parameter is being estimated then there is nothing to which a confidence interval can attach.
Contents of a defensible study
Report the PMP as a depth with an exceedance probability and a stated climate period, not as an upper limit. If the study cannot supply the probability, say so explicitly rather than leaving the reader to assume one.
Derive an AEP curve alongside the deterministic PMP. The deterministic value remains the design standard in most regimes; the curve is what makes the result usable in risk-informed decision making. Fit it using threshold exceedance, sometimes called peaks over threshold, rather than annual maxima. Annual maxima mix storm types, and including events from types with lighter tails biases the shape parameter that governs the far tail, which is the part of the curve that matters here.
Mark AEP estimates that extend beyond the length of the underlying record as extrapolated and indicative only, at the point of use rather than in a general caveat.
The stationarity assumption is contrary to multiple lines of evidence, and neglecting climate change may underestimate future risk. The review holds that where no model-based scaling exists for the region, Clausius-Clapeyron scaling of approximately 7% per degree applied to a stated warming increment is the simplest defensible interim adjustment.
I am not a great enthusiast for the simplification.
Warming does not translate into more rainfall everywhere and a PMP estimate is usually followed by a PMF evaluation in which flow does not grow linearly with rainfall. It should be presented as a sensitivity case, not as a projection.
If PMP is a depth at an extremely low AEP, someone has to specify which AEP is acceptable for which class of structure. That is a societal risk judgement, not a project decision. The review recommends that US agencies develop such guidance, and I expect others will wait to see what emerges and follow.
The other gap is the science. The longer-term direction is model-based, using kilometre-scale ensembles to construct the precipitation distribution directly and taking PMP as the depth at a specified very low AEP. General circulation models cannot substitute for this, since at their resolution convection is parameterised rather than resolved, and convection is what produces PMP-magnitude rainfall on small catchments. Ambitious, but doable.
References
- Hansen, E.M., Fenn, D.D., Corrigan, P. and Vogel, J.L. (1994) Probable Maximum Precipitation, Pacific Northwest States. Hydrometeorological Report No. 57. Silver Spring, MD: National Weather Service.
- Hershfield, D.M. (1961) Estimating the probable maximum precipitation. Journal of the Hydraulics Division, ASCE, 87(HY5), 99-116.
- Herschy, R.W. (2003) World Catalogue of Maximum Observed Floods. IAHS Publication 284.
